An Archive for Preprints in Philosophy of Science ...



Version Oct. 11, 10

The Ultimate Argument against Convergent Realism and

Structural Realism: The Impasse Objection

Paul Hoyningen-Huene

Institute of Philosophy, Leibniz Universität Hannover

I will first deal with all forms of convergent realism. I will then turn to the variety of realisms that do not explicitly claim some sort of convergence but exploit some kind of stability in a sequence of theories; this includes structural realism. Convergent realism is a doctrine (or rather a family of doctrines) that roughly states that we are fairly safe to accept the following three propositions (compare, e.g., Sankey (2004)):

i) Our best mature scientific theories refer to something which is really out there.

ii) In the course of scientific development, during which the empirical predictions of these theories continuously improve, the quality of their propositions about what they refer to also becomes better and better.

iii) In the limit, the sequence of our best mature scientific theories converges to a (or even the) true theory. Whether or not this limit is or will be practically attainable is not relevant. However, the existence of this limit is relevant because if there were no such limit it would not make sense to say that our best mature scientific theories approximate the truth (as convergent realists do).

In the following, I shall drop the cumbersome clause “that we are fairly safe to accept” these propositions which takes care of their general fallibility. I shall simply say that convergent realism states the three above-mentioned propositions without meaning to deny their general fallibility.

The very general characterization of convergent realism given above leaves open the question of what the nature of the things referred to by the theories is. This is because this characterization is intended to cover the two most popular forms of convergent realism at the same time: convergent entity realism and convergent structural realism (on the difference see, e.g., Ladyman (2009)). Convergent entity realism claims that the things our best mature theories correctly refer to are certain (theoretical) entities whereas convergent structural realism claims that these things are (mathematical) structures. There are several variants of these positions together with several arguments supporting them. I shall, however, not address these explicative and argumentative variants in this paper because my claim is that the ultimate argument against convergent realism (to be explicated below) is neutral with respect to them. Before substantiating this claim, I shall review two problems of convergent realism that pose serious although not necessarily fatal difficulties to any form of it (for an extremely condensed exposition of these problems, see Hoyningen-Huene and Oberheim (2009), fn. 7). Because they are not fatal problems, I shall not attempt their definitive evaluation but will be happy to leave their ultimate status open. For the sake of argument, however, I will later assume that these problems can be entirely solved.

First, there is a mathematical problem. In discussing convergent realism, we are considering a sequence of theories whose convergence is claimed. Whatever our criteria of individuation of theories are, the number of theories considered is fairly small. Whatever “fairly small” may mean here, it is certainly a finite number, and having the impression of convergence of a (potentially infinite) sequence on the basis of a finite number of its elements is always risky. Perhaps this objection can be defused by the assumption that the yet unknown elements of the sequence will continue the already visible trend because otherwise they would not be accepted by the relevant scientific communities. It is difficult to judge whether this argument is too optimistic or not if understood descriptively, or whether it should be given a normative twist in order to save it from the vicissitudes of future history. I shall leave the argument at that.

Second, there is a conceptual problem. To speak of the convergence of sequence of theories toward some limit presupposes a space of theories that comprises all elements of the sequence. Although the limit itself – a (or the) true theory – does not have to be an element of this theory space itself, all the theories approximating this true theory to any degree have to be. Thus, although we certainly do not know what the ultimate true theory or theories look like, we must be able to oversee all approximations to it in order to construct the relevant theory space. This is certainly not a trivial task. For instance, would the late 19th century physicists attempting to construct such a theory space have been able to include in this theory space quantum theory, general relativity and the standard model of particle physics? This is doubtful. However, we may entertain the optimistic vision that although we are actually unable to construct the relevant theory space, in the course of time we will learn more and more about the theories approximating truth better and better. This will enable us to continuously widen the theory space in question in which the (presumably convergent) theory trajectory achieved up to that point will be documented.

In addition to the theory space itself, we need a metric (or distance function) on it relative to which convergence can be stated. Clearly, this metric will depend on the kind of convergence that is claimed, namely whether we claim convergent entity realism or convergent structural realism. The definition of such a metric may be a formidable technical problem but I see no argument why this task should be impossible in principle. Of course, given the metric we will not be able to directly show the decreasing distance of the elements of the sequence to the true theory because we don’t know what the true theory is (we don’t even know whether it is an element of our theory space). But we should be able to demonstrate the convergence of the theory sequence – if it exists – by Cauchy’s criterion, i.e. roughly speaking, by diminishing distances between the elements of the sequence the further we progress (see Rosenberg (1988), pp. 171-4). Of course, the mathematical problem discussed above reappears here: successfully applying Cauchy’s criterion to a finite number of elements of the sequence does not, strictly speaking, say anything about convergence at all. But we shall assume in the following that we can somehow overcome this difficulty. This means the following: If there is an actually convergent sequence of theories, then we are able to demonstrate (or at least make sufficiently plausible) its convergence by using our metric in the theory space and the Cauchy criterion.

In order to formulate the ultimate argument against convergent realism, let us make two assumptions for the sake of argument. Let us first assume that all the difficulties mentioned above can be resolved. Thus we assume that we can define a theory space big enough to contain all approximations to the true theory, and that we can define a metric appropriately measuring the distance of any element of the theory space to the true theory (related to entities for convergent entity realism or related to structures for convergent structural realism). In other words, we know exactly what we are talking about when we speak about convergence of theories to a limiting theory. Let us now apply our formal instrument – the theory space with appropriate metric – to a sequence of actually existing theories that is a candidate for convergence to the truth. In other words: this sequence displays enough continuity regarding entities (for entity realism) or structures (for structural realism) and a continuous improvement of empirical predictions of the theories in the sequence. Let us now, secondly, assume that the result of the application of our formal instrument is that the sequence indeed converges, thus vindicating the convergent realist’s intuitions on a much more formal and therefore secure level.

To summarize: we are conceding to the convergent realists almost everything they need. The notion of convergence of theories has been made sufficiently precise by means of a theory space and an appropriate metric, and we have a sequence (or even sequences) of mature scientific theories that do indeed converge according to the formal apparatus. For the sake of argument, we make these concessions both to the convergent entity realists and to the convergent structural realists. The only remaining question is this: What can we say about the limit? Of course, the convergent realists will surely want to say that the limit is the true theory but there will be a difference in emphasis between the convergent entity realist and the convergent structural realist, respectively. For the convergent entity realist, the emphasis will be on a truthful representation of the entities populating the universe, whereas for the convergent structural realist the emphasis will be on the truthful representation of the (mathematical) structure of the universe. For both of them, the stability of entities or structures in the course of the actual scientific development until today has been the indicator that science got it right, at least approximately, regarding these entities or structures (see assumption (i) at the beginning of this paper). Therefore, the limit of the sequence of theories should be a theory that gets the entities or structures entirely right – the true theory.

However, there is an objection. For the answer that the limit will be a (or the) true theory to be convincing, the following alternative candidate for the limit must be excluded. Instead of approaching the true theory, the sequence of theories could approach a theory – call it the limit theory – that is much better than our current theories regarding empirical predictions, but is still fundamentally wrong. What does this mean?

• The limit theory is much better than our current theories regarding empirical predictions would mean, for instance, that all its quantitative empirical predictions are correct with a relative accuracy of 10-100.

• “Fundamentally wrong” would mean for the convergent entity realist that the entities postulated by the limit theory would be so different from the real entities (described by the true theory) that the limit theory’s entities could not count as approximations to the real entities. In other words: At least some of the terms of the limit theory do not refer to the real entities.

• “Fundamentally wrong” would mean for the convergent structural realist that the structure of the limit theory would be so different from the structure of the true theory that it would be impossible to say that the limit theory’s structure is preserved in the true theory’s structure.

The limit theory to which our best mature theories converge would therefore be an impasse from which it would be impossible to get at the true theory by further gradual improvements, keeping the basic entities stable, or finding a new structure of which the old structure is a special case, respectively. The objection is thus that the limit theory (whose existence has been conceded to the convergent realists for the sake of argument) could be fundamentally different from the true theory. As we have no means whatsoever to say anything substantial about the limit theory apart from the fact that it is the limit of the sequence our best mature theories, we cannot rule out that the limit theory is indeed an impasse – ontologically or structurally far away from the true theory. The (conceded) convergence of our best mature theories is therefore not a reliable indicator that these theories got the real entities or the real structures approximately right. This is the impasse objection to convergent realism.

Let us now turn to the variety of realisms that do not explicitly claim some sort of convergence but exploit some kind of stability in a sequence of theories in order to identify the things that can be realistically interpreted. The main types of this form of realism are all kinds of structural realism that endorse the “structural continuity claim” (Votsis (in press)). However, any argument that infers from some kind of stability in a sequence of theories (stability of entities or of structures) that the stable elements can be realistically interpreted falls prey to the impasse objection. The impasse objection states that the observed stability could also stem from a theory that is empirically much better than current theories but still fundamentally at odds with reality (with entities or structures). It thus turns out that the apparent advantage of structural realism over entity realism, namely, that structures are much more stable than entities in the course of scientific development (see, e.g., Worrall (1996 [1989]), Ladyman (2009)), is of no help against the impasse objection. The sobering result is this: given the impasse objection, stability of structure does not support structural realism.

Let me now discuss three possible counter-objections to the impasse objection. First, one might be tempted to neutralize the impasse objection by assimilating it to extremely general and fundamental skeptical arguments like Cartesian doubt or doubt about the existence of an external world. This would be inappropriate, however, because the impasse objection puts into doubt the very specific transition from the (conceded) fact of convergence to a property of the limit, namely, to be the true theory. The impasse objection specifically states that this is a non sequitur. It thus belongs to a category of very specific arguments different from the class of very general skeptical arguments.

Secondly, entity realists may concede the logical correctness of the impasse objection. However, they may hold that because of the stability of postulated entities in the sequence of theories, i.e. in several theories, it is more likely that the entities postulated in our best mature theories are real and that therefore, the limit theory is indeed a (or the) true theory. This, however, is a fallacy.[1] The stability of entities in the elements of the sequence of theories is simply a reflection of the fact that the sequence converges. The stability is thus not remarkable and it is especially no indicator of the truth of the limit theory. – There is a similar counter-objection of the structural realist that can be answered analogously.

Thirdly, it could be asked whether the no-miracles-argument could overcome the difficulties posed to realism by the impasse objection. The no-miracles-argument, sometimes called “the ultimate argument” for realism (van Fraassen (1980), p. 39; Musgrave (1988)), basically states that the only explanation for the success of science is realism. In the most refined and most defensible form of the argument, the “success of science” is spelled out as the production of use-novel predictions by theories. “Use-novel predictions” have not been used in the construction of the theory in question so it comes as a surprise that it is capable of predicting them, suggesting that this is due to the theory getting something fundamentally right.

The impasse objection states that the limit theory that provides the visible stability to the theory sequence in question may be fundamentally different from the true theory. The miracle argument would counter that the incredible success of the limit theory, say, as in the example above, a relative accuracy of 10-100, would be a miracle if this theory were not very close to the true theory. However, this would be the application of an unsophisticated form of the miracle argument equating the success of science with unqualified predictive success. As the recent discussion of the no-miracles-argument has shown that it works, if it works at all (which has been doubted by several authors for different reasons, see among many others, e.g. Hoyningen-Huene (2009), Frost-Arnold (2010)), only on the basis of use-novel predictions that a theory produces (Worrall (1985); Worrall (1989), pp. 148-9; Carrier (1991), pp. 26-28; Earman (1992), pp. 114-5; Leplin (1997); Psillos (1999), p. 106; Psillos (2006), p. 133). However, there is no indication whatsoever that the limit theory will be capable of use-novel predictions; thus the no-miracles-argument does not apply to it, even according to its defenders.

Of course, I cannot claim that these are the only possible counter-objections to the impasse objection. Therefore, it is certainly not excluded that the given “ultimate” argument will share the fate of other supposedly ultimate arguments, namely, to be transitory.

Acknowledgements. I wish to especially thank Thomas Reydon for inspiring remarks on an earlier draft of this paper, but also Simon Lohse, Eric Oberheim, and Nils Hoppe for comments.

References

Baxter, R.J. (1977): "Soluble models on the triangular and other lattices". In Annals of the Israel Physical Society, Vol. 2. Statistical Physics, Statphys 13, Proceedings of the 13th IUPAP Conference held 24-30 August, 1977 at the Technion Israel Institute of Technology, edited by D. Cabib, C. G. Kuper and I. Riess. Bristol: Hilger, pp. 37-47.

Carrier, Martin (1991): "What is Wrong With the Miracle Argument?". Studies in the History and Philosophy of Science 22:23-36.

Earman, John (1992): Bayes or Bust?: A Critical Examination of Bayesian Confirmation Theory. Cambridge Mass.: MIT Press.

Frost-Arnold, Greg (2010): "The No-Miracles Argument for Realism: Inference to an Unacceptable Explanation". Philosophy of Science 77 (1):35-58.

Hoyningen-Huene, Paul (2009): "Reconsidering the miracle argument on the supposition of transient underdeterminationi". Synthese DOI 10.1007/s11229-009-9600-2.

Hoyningen-Huene, Paul, and Eric Oberheim (2009): "Reference, ontological replacement and Neo-Kantianism: a reply to Sankey". Studies In History and Philosophy of Science Part A 40 (2):203-209.

Ladyman, James (2009): "Structural Realism". In Stanford Encyclopedia of Philosophy, edited by E. N. Zalta. URL: .

Leplin, Jarrett (1997): A Novel Defense of Scientific Realism. Oxford: Oxford University Press.

Musgrave, Alan (1988): "The Ultimate Argument for Scientific Realism". In Relativism and Realism in Science, edited by R. Nola. Dordrecht: Kluwer Academic.

Psillos, Stathis (1999): Scientific Realism: How science tracks truth. London: Routledge.

Psillos, Stathis (2006): "Thinking About the Ultimate Argument for Realism". In Rationality and Reality: Conversations with Alan Musgrave, edited by C. Cheyne and J. Worrall. Berlin: Springer, pp. 133-156.

Rosenberg, Jay F. (1988): "Comparing the incommensurable: another look at convergent realism". Philosophical Studies 54 (2):163-193.

Sankey, Howard (2004): "Scientific Realism: An Elaboration and a Defence". In Knowledge and the World: Challenges Beyond the Science Wars, edited by M. Carrier, J. Roggenhofer, G. Küppers and P. Blachard. Berlin: Springer, pp. 55-80.

van Fraassen, Bas C. (1980): The Scientific Image. Oxford: Clarendon.

Votsis, Ioannis (in press): "Structural Realism: Continuity and its Limits". In Scientific Structuralism, edited by A. Bokulich and P. Bokulich. Dordrecht: Springer.

Worrall, John (1985): "Scientific discovery and theory-confirmation". In Change and progress in modern science, edited by J. C. Pitt. Dordrecht: Reidel, pp. 301-332.

Worrall, John (1989): "Fresnel, Poisson, and the White Spot: The Role of Successful Predictions in the Acceptance of Scientific Theories". In The Use of Experiment. Studies in the Natural Sciences, edited by D. Gooding, T. Pinch and S. Schaffer. Cambridge: Cambridge University Press, pp. 135-157.

Worrall, John (1996 [1989]): "Structural Realism: The Best of Both Worlds?". In The Philosophy of Science, edited by D. Papineau. Oxford: Oxford University Press, pp. 139-165 (originally in Dialectica 43: 99-124 (1989)).

-----------------------

[1] This is a situation that also occurs in the sciences. For instance, in the mid 1970s there was a variety of apparently different two-dimensional lattice models that agreed in their predictions of certain crucial thermodynamic properties. Therefore, these predictions appeared to be model independent and thus especially trustworthy. However, at a conference in 1977, the Australian physicist Rodney J. Baxter presented a model that showed that most of the current models were special cases of his own more general model (see Baxter (1977)). Consequently, the confidence in the model-independency of the predictions due to their production by apparently different models immediately collapsed.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download